You mention in conversation to your friend, "A carat is for diamonds, while a karat measures gold's purity".
Now if your friend is not well versed in the jargon of jewelry, you cannot in good faith laugh at them when they eye their vegetable basket suspiciously, wondering, what on earth have carrots got to do with diamonds and gold? Perhaps you want to explain it in a more clear fashion to your friend or perhaps you are the friend in question. In any case you are right where you need to be.
Now, poor carrots have got nothing to do with this mess, save for a similar sounding name, but another food source does. Carob tree is a native of Mediterranean and Middle East. Its seeds were used as measurement of weight many centuries ago because people that Carob seeds did not vary in weight. This one should note is not correct, as carob seeds are not any more invariant in weight than seeds of any other kind.
However, the misinformation stuck and carob seeds became a standard in the ancient world for weighing small quantities for a long time. Constantine the Roman emperor, issued, a practically, pure gold coin in his reign, called Solidus, which was divided into 24 equal parts, named Siliqua. Now, siliqua happened to be equal to a karat in weight, hence, karat took on a sense of "a proportion of one twenty-fourth, a twenty-fourth part," especially in expressing the fineness of gold when used as jewelry, and thus it became a measure of gold purity.
If the previous sentence was a head scratcher then do not worry, we will explain it further. Karat just measures the percentage of pure gold in a given piece of...gold. A 24 Karat gold piece is 99.9 percent gold (note we cannot completely keep impurities out) while 18 karat gold has 18 parts gold and 6 parts other alloys, meaning that by percentage, 75% of it is gold. Similar calculations can be done for 16K, 14K and so on. Alloys are added to give the gold different physical properties, such as, color, durability, hardness about which we will go into its details another time.
Something that might confuse people is the idea that, two pieces of jewelry with the same karat number can have different weights. Remember, a karat is the measure of how much gold by proportion is in a given piece of jewelry. It does not tells us the weight of that jewelry or the gold in it, if the only thing we know about it is its karat. Take, for instance, our gold wedding bands shown below, one is a 18K white wedding band and weighs 3.12 grams, whereas the 18K Rose band besides it, is 13.47 grams. The karat number tells us the percentage of gold in these jewelry pieces.
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Now that we know what a karat is, it is time, to tackle the other term, Carat. When we talk about a diamond and its carat, what we are discussing is the weight of the diamond. This is an important difference between the karat of gold and the carat of diamonds. Everyone, eventually, realized that Carob seeds were too unreliable a weighing measure and they had to standardize the unit. Different standard weights were adopted for Carat over the centuries but in 1907, it was decided that the Carat would be 200 milligrams (0.2 grams). So when we say, that a particular diamond is X carat. What we are describing is the weight of that diamond. A 1 carat diamond weighs 0.2 grams and a conversely a 1 gram diamond is 5 carat.
So far so good right? If you are familiar with terminology surrounding diamonds, you might be wondering what is CTW or TCW. These both refer to the total carat weight of diamonds in a given piece of jewelry. Many jewelry pieces have more than one diamonds and CTW is a convenient way to express the weight of diamonds in them. Take for instance the two pieces below. The necklace on the left has only a single piece of diamond of 1/4 CTW while the earrings have, multiple whose CTW is 1/4. Meaning the total weight of diamonds is equal in both.
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Great, now you know what karat and carat and from where did they originate. The only term left to explain is caret. Rest assured, the term is as far away from the world of jewelry as possible; Caret is the name for the character: ^.